A simple numerical experiment on the dust temperature bias for Lyman break galaxies at z ≳ 5

Abstract Some studies suggest that the dust temperatures (Td) in high-redshift (z ≳ 5) Lyman break galaxies (LBGs) are high. However, possible observational bias in Td is yet to be understood. Thus, we perform a simple test using random realizations of LBGs with various stellar masses, dust temperatures, and dust-to-stellar mass ratios, and examine how the sample detected by ALMA is biased in terms of Td. We show that ALMA tends to miss high-Td objects even at total dust luminosity LIR > 1011 L⊙. LBGs are, however, basically selected by the stellar UV luminosity. The dust-temperature bias in a UV-selected sample is complicated because of the competing effects between high Td and low dust abundance. For ALMA Band 6, there is no tendency of high-Td LBGs being more easily detected in our experiment. Thus, we suggest that the observed trend of high Td in z ≳ 5 LBGs is real. We also propose that the 450 $\rm {\mu m}$ band is useful in further clarifying the dust temperatures. To overcome the current shallowness of 450 $\rm {\mu m}$ observations, we examine a future Antarctic 30-m class telescope with a suitable atmospheric condition for wavelengths $\lesssim 450~\rm {\mu m}$, where the detection is not confusion-limited. We find that, with this telescope, an LIR-selected sample with log (LIR/L⊙) > 11 is constructed for z ≳ 5, and detection in the intermediate-M⋆ (stellar mass) range [9 < log (M⋆/M⊙) < 9.5] is much improved, especially at high Td.